Browsers sandbox most things, including storage, by origin (essentially the domain, plus protocol and port). See the Same-origin policy for more details.
In practice this means if your website runs on example.com, you can access anything else that happens on example.com, but not anything else that happens on other websites like on construct.net. It's an important security barrier to ensure things like other websites cannot steal your login details for other sites. It's possible to get other domains to intentionally share their information if they are specifically designed to do so, but it's technically quite complicated, and there are all sorts of privacy, security and anti-tracking hoops to jump through.